OFFSET
0,2
EXAMPLE
For a 4 X 4 matrix the 16 possible permanents and their multiplicities are:
{{0, 27713}, {1, 13032}, {2, 10800}, {3, 4992}, {4, 4254}, {5, 1440}, {6, 1536}, {7, 576}, {8, 648}, {9, 24}, {10, 288}, {11, 96}, {12, 48}, {14, 72}, {18, 16}, {24, 1}}
From M. F. Hasler, Jan 19 2026: (Start)
For n = 3, we have a(3) = 6 since all values from 0 to 3! = 6 occur, except for 5. Matrices that yield 0, 1 and 3! are obvious (e.g., O, I and the "all ones" matrix). Matrices with only one zero give 4 (as can easily be seen from the definition). Matrices with just two zeros, not in the same row or column, give 3. Matrices with two zeros in the same row or column yield 2.
For n = 5, all values from 0 through 40 except for 27, 35 and 37 occur, and also 42, 44, 46, 48, 50, 53, 54, 60, 64, 72, 78, 96 and 120. (End)
PROG
(PARI) /* Very naïve brute force script that creates all relevant matrices, computes their permanent and marks the seen values. For illustration (n < 6) only. */
A087983(n)={ my(map=1/* bitmap of values seen */, Mn=2^n-1, M=matrix(n, n), row=1, min_row=vector(n, i, 2^(i-1)), rows=min_row); n&& while(row/*to increment*/, if( row==n, for(j=rows[n], Mn, M[n, ]=binary(j); map=bitor(1<<matpermanent(M), map)), rows[row] < Mn, rows[row]++; until(row==n, M[row, ] = Vec(binary(rows[row]), -n); rows[row+1]=max(rows[row], min_row[row++]) ); next); row--); hammingweight(map)} \\ M. F. Hasler, Jan 18 2026
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Wouter Meeussen, Oct 29 2003
EXTENSIONS
a(6) = 220 from Gordon Royle, Nov 05 2003
a(7) from Giovanni Resta, Mar 29 2006
a(0) = 1 prepended by Alois P. Heinz, Apr 28 2020
a(8) from Minfeng Wang, Oct 04 2024
a(0)-a(8) verified by Brendan McKay, Jan 19 2026
STATUS
approved